Respecting causality segmental time-domain training accelerates physics-informed DeepONet on time-dependent PDEs

Physics-informed deep operator network (DeepONet) has achieved remarkable success in solving partial differential equations (PDEs), yet its convergence is often slow. To address this issue, we have proposed a causality segmental time-domain training method to accelerate physics-informed DeepONet. The temporal horizon of the operator learning task is partitioned into multiple subintervals. To enforce causality during training, each temporal subinterval is assigned a weight that adapts to the evolution of the residual loss. This segmental weighting prioritises early segments until their residuals are sufficiently reduced, after which later segments are progressively optimised. Compared with the standard physics-informed DeepONet, the proposed method has significantly accelerated convergence and reduced prediction error. A series of numerical experiments has validated the effectiveness of the proposed training method. The causality segmental time-domain training method attains a balance between respecting temporal causality and leveraging the network's global optimisation capabilities within each segment, markedly enhancing the training efficiency and predictive accuracy of the physics-informed DeepONet.